Piezoelectric crystal apparatus



Oct. 21, 1941. w. P. MASON PIEZOELECTRIC CRYSTAL APPARATUS Filed Oct.19', 1940 2 Sheets-Sheet 1 HQ TOWARD OBSERVER TO OSCILLATOR OR FILTERCIRCUIT lNl ENTOR W P MA 5 ON FIG-4 A T TORNFV Oct. 21, 1941.

W. P. MASON PIEZOELECTRIC CRYSTAL APPARATUS Filed Oct. 19, 1940 2sheets-sheet 2 FIG. 7

FREOUENCI IN KILOCYCLET PER SECOND PER CENT/METER ELEKNTZRY LENGTH uINVENTOR memso/v .w.%.6wwx

A T TORNEY Patented Oct. 21, 194i PIEZOELECTRIC CRYSTAL APPARATUS WarrenP. Mason, West; Orange, N. J assignor to Bell Telephone LaboratoriesIncorporated, New York, N. Y., a corporation of New York ApplicationOctober 19, 1940,-'Serial No. 361,857

' 13 Claims. o]; 1711-427) This invention relates to piezoelectriccrystal apparatus and particularly to harmonic longitudinal modepiezoelectric quartz crystal elements adapted for use as circuitelementsin such systems as electric wave filter systems and radiofrements of low temperature coeflicient of frequency are described whichhave much the same frequency characteristics as those of the formerapplication but differ therefrom as to orientation, dimensional ratio,and impedance. I

One of the objects of this invention is to obtain relatively highfrequency piezoelectric crystal elements having a low or substantiallyzero temperature coefficient of frequency and a low impedance.

' Another object of this invention is to obtain relatively highfrequency piezoelectric crystal elements of nearly constantvibrational'frequency throughout a wide range of ordinary temperatures'Another object of this invention is to obtain high frequencypiezoelectric crystal elementssubstantially free from interferingvibrational modes and of low temperature coeflicient of frequency. Insingle side-band short wave radio systems and in radio broadcasting andother systems such as wide band filter systems at high frequencies, forexample, it is often desirable to obtain a constant frequency which doesnot vary appreciably with temperature change. For the relatively lowerfrequencies, this requirement is met by fundamental mode crystalsof thetype described in my U. S. Patent 2,204,762 dated June 18, 1940; but forthe relatively higher frequencies, such fundamental mode crystals insome instances may be inconveniently small in size. It isthe purpose ofthis invention to provide harmonic mode crystals of low or substantiallyzerotempe'rature coefiicient of frequency which are capable of givingvery good stability for frequencies up toseveral megacycles per second,the harmonic mode quartz crystal elements having such relatedorientation, dimensional ratio' and vibrational mode as to obtain thedesired low or substantially zero temperature coemcient of frequencywithin temperature ranges that may occur in practice.

In accordance with this invention, a relatively thin piezoelectricquartz crystal plate of suitable orientation with respect tothe X, Y andZ axes thereof,and of a suitable dimensional ratio corresponding to theorientation, may be subjected to a thickness direction or Y electricfield and vibrated atan odd or an even harmonic resonance frequencydependent mainly upon the length dimension of the crystal plate in acoupled mode of motion which consists of a harmonic longitudinal orextension-al vibration along such length dimension giving the desiredharmonic resonance frequency referred to and mechanically coupledtherewith trans-verse vibrations along the width dimension of thesubstantially rectangular major plane of the crystal plate. The width ortransverse vibrations referred to are in the nature of third overtoneedge bulge vibrations alternately -bulging outwardly and inwardly theopposite elementary portions of the edges of the crystal plate. Theorientation of the crystal plate may be any of several, the lengthdimension of the crystal plate being in every such case inclined eitherabout 45 degrees, or' alternatively about 135" degrees, with respect to'an electric axis X, and the major plane being in every case parallel ornearly parallel to' such X axis and inclined with respect to the opticaxis Z at any angle between about +43 and +52 degrees. Such quartzcrystal plateswhen suitably proportioned as' to relative width andlength dimensions produce,

for theharm'onic'longitudinal mode resonant fr'equeriey mentioned of anyorder; a low or substantially zero temperature coefficient of frequencyat temperatures within a temperature range between --40 and +100 C. In"a particular species where the major plane of the crystal plate isinclined'about +4430 with respect to the Z axis, and the fundamental orelementary length Z of each of the elementary areas of the harmonicmo'de crystal plate is related to the above-mentioned" width dimension Win the ratio of about the longitudinal mode harmonic resonant fre-'quency referred toof any order such as the third or fifth harmonicfrequency, has a very constant or flat frequency characteristicthroughout a range of temperatures from about 5 to 45 C.,

the mid-temperature of such constant frequency range being about +25' C.

To further reduce the temperature coefficient of frequency of suchcrystals operating at or near the resonant frequency and having a smalltemperature-frequency coefficient, a condenser of small capacity may beconnected in series circuit relation with the crystal, the condenseritself having a temperature coefficient of capacitance of such magnitudeand sign with respect to that for the crystal, that it will balance thatof the resonant frequency of the crystal thereby reducing the over-alltemperature coefficient of frequency of the combination.

For a clearer understanding of the nature of this invention and theadditional features and objects thereof, reference is made to thefollowing description taken in connection with the accompanyingdrawings, in which like reference characters represent like or similarparts and. in which:

Figs. 1 and 2 are enlarged views of an harmonic longitudinal modepiezoelectric quartz crystal plate embodying this invention, Fig. 1being a projected edge view taken in the horizontal direction indicatedby the arrows l-l of Fig. 2, and Fig. 2 being a major face view'taken inthe direction indicated by the arrows 2-2 of Fi 1';

Fig. 3 is a major face view of a quartz plate similar to that of Fig. 2but having an alternative 45-degree orientation angle with respect tothe X axis; a

Fig. 4 is an edge view of the crystal plate of Figs. 1 to 3 providedwith electrodes and electrode connections for fifth harmoniclongitudinal mode operation;

Fig. 5 is a developed view of an electrode and electrode interconnectionplating arrangement that may be utilized on the crystal element of Figs.1 to 4; Fig. dis a graph showing the relation between the orientationangle and the desired longitudinal mode resonant frequency of quartzcrystals in accordance with this invention;

Fig. {7 is a graph showing related values of orientation angle anddimensional ratio that may be utilized to obtain a zero temperature.coefiicient of frequency in quartz crystals embodying this invention,for o angles in the region of substantially +44 to +52 degrees.

This specification follows the conventional terminology as applied tocrystalline quartz which employs three orthogonal or mutuallyperpendicularX, Y and Z axes, as shown in the drawings, to designate anelectric, a mechanical and the optic axes, respectively, ofpiezoelectric quartz crystal material, and which employs threeorthogonal axes X, Y and Z to designate the directions of axes of apiezoelectric body angularly oriented with respect to such X, Y and Zaxes thereof. Where the orientation is obtained by doubl'e'rotations ofthe quartz crystal element I, one rotation being in effect substantiallyabout an electric axis X, and the other about another axisfY of thepiezoelectric body as illustrated in Figs. 1 and 2, the orientationangles (p and 0 respectively, designated in degrees the effectiveangular position of the crystal plate I as measured from the optic" axisZ and from the orthogonal electric axis X, respectively. The length axisX shown in Figs. 2 and 3 indicates the result of a second rotation.

Quartz crystals may occur in two forms, namely,' right-handed andleft-handed. A righthanded quartz crystal is one in which the plane ofpolarization of a plane polarized light ray traveling along the opticaxis Z in the crystal is rotated in a right-hand direction, or clockwiseas viewed by an observer located at the light source and facing thecrystal. This definition of right-handed quartz follows the conventionwhich originated with Herschel. Trans. Cam. Phil. Soc. vol. 1, page 43(1821); Nature vol. 110, page 807 (1922); Quartz Resonators andOscillators, P. Vigoureux, page 12 (1931). Conversely, a quartz crystalis designated as left-handed if it rotates such plane of polarizationreferred to in the left-handed or counter-clockwise direction, namely,in the direction opposite to that given hereinbefore for the righ-handed crystal.

If a compressional stress or a squeeze be applied to the ends of anelectric axis X of a quartz body I and not removed, a charge will bedeveloped which is positive at the positive end of the X axis andnegative at the negative end of such electric axis X, for eitherrighthanded or left-handed crystals. The magnitude and sign of thecharge may be measured in a known manner with a vacuum tube electrometerfor example. In specifying the orientation of a right-handed crystal,the sense of the angle p which'the new axis Z makes with respect to theoptic axisZ as the crystal plate is rotated in effect about the X axisis deemed positive when, with the compression positive end of the Xaxispointed toward the observer, the rotation is in a clockwise direction asillustrated in Fig. 1. A counter-clockwise rotation of such aright-handed crystal about the X axis gives rise to a negativeorientation angle o with respect to the Z axis. Conversely, theorientation angle of a left-handed crystal is positive when, With thecompression positive end of the electric axis X pointed toward theobserver, the rotation is 'countereclockwise, and is negative when therotation is clockwise. The crystal material illustrated in Figs. 1 to 3is right-handed as the term is used herein. For either right-handed orlefthanded quartz, a positive angle (p rotation of the Z axis withrespect to the Z axis as illustrated in Fig. 1 is toward parallelismwith the plane of a minor apex face of the natural quartz crystal, and anegative (p angle rotation of the Z axis with respect to the Z axis istoward parallelism with the plane of a major apex face of thenatural'quartz crystal.

Referring to the drawings, Figs. 1 and 2 are respectively an edge viewand a major face view of aright-handed relatively thin piezoelectricquartzcrystal plate i of substantially rectangular parallelepiped shapehaving an over-all length dimension L, a width dimension W which isperpendicular to the length dimension L, and 'a thickness or thindimension T which is perpendicular to th length dimension L and thewidth dimension W. As shown in Fig. 1, the major plane and the oppositemajor faces 2 and 3 of the crystal plate I may be parallel or nearlyparallel to an electric or X axis of the quartz material and inclinedwith respect to the optic axis Z at a 1angle of about +44 30 as measuredbetween the Z and Z axes in a plane which is perpendicular tothe X axisand to the major plane of the crystal plate I. Small angle departures upto 5 degrees or more, for example of the major faces 2 and 3, fromparallelism with respect to the X axis do not greatly alter thecorresponding 4: angle required to obtain the low or substantially zerotemperature coefiicient of frequency. Since the minor apex faces of thenatural quartz crystal from which the quartz plate I is cut occur at aangle of about +38 degrees with respect to the optic axis Z, thepositive sense or the w ansleis equivalent to a rotati n ab ut the Xaxis from the Z axis toward parallelism with the plane. of a minor apexface for either right-handed or left-handed quartz.

In. .Fi 1. the X axis isnerpendicular to the plane of the drawin s withthe compression positive end or the X axis pointed towards the observer,and is also perpendicular to both the Y and Z axes. The over-all lengthdimension L of the crystal plate. I lying along the axis X" as shown inFigs. 2and 3.: may be inclined at an an le of about 4 5 degrees withrespect to the aboveementioned X axis in either direction as i1lustrated by the alternative 0 angle orientations shown in Figs. 2 and3. 7 While the X" axis len th dimension L of the crystaliplate- I ofFig. 2 is. inclined at a difierent 45-.degree a angle with respect tothe X axis than that of Fig. 3, it will be understood that either ofthese 45adegree po sitions forthe angle. a. may be used alternativelywith any of'the angles. disclosed herein. Suitable conductiveclectrodessuch as the electrodes A in Figs. 2 and 4 may be. placed on, adiacent.or. be for-med integral with the opposite majorfaces 2. and 3 of thecrystal plate 1 to apply harmonic modeelectric field excitation to thequartz. plate t in the direction or the thickness dimension T, and bymeans of any suitable circuit such as, for example, a filter or anoscillator circuit, the. quartz plate i. may be vibrated in the desiredlongitudinal mode of motion at an odd or an even harmonic vibrationresponse frequency which depends mainly upon and varies inversely as.the length dimension L and the ele mentary length dimension Z It. willbe understood; that thetcrystalplate I. may be operated in any desiredodd or even harmonic longitudinal mode along the. length dimension L- bymeans of a plurality of pairs. or equal area opposite electrodes tdisposed adjacent the, opposite maj'or races 2 and 3 of the crystal;plate l. The electrodes. 4. may be interconnected as illustratedschematically in Fig. 4- so that all positive 4+) electrodes:areconnected together and all negatime 6-3). electrodes. are connectedtogether but no positive electrode is connected with a negativeelectrode. The number of pairs of opposite electrodes 4 tobe usedcorresponds to thenumerical order of the desired harmonic which may beanyodd or even overton ofi the fundamental mode. For example, to. drivethe crystal E in the fifth harmonic longitudinal mode, five pairs ofequal area opposite electrodes 4 may beutilized as il lustr'atecl inFigs. 2 and 4; and similarly to drive the crystal plate L third harmoniclongitudinal vibrations along the length dimension L, three pairs ofopposite electrodes which may partly or nearly vvhol'ly cover the equalelementary lengths l of the major faces 2 and 3- may beutilized: Theodd.- harmonic mode is ofspecial interest since then the crystal plate Imay be clamped at its geometrical center It at the centers of themiddl'e pair of opposite electrodes 4. Reference is made to my UnitedStates Patent No. 2,185,599 granted January 2, 1940: on application-Serial No. 65,022, filed. February Z t, 1933 for examples or harmonicmode. electrode and electrode connection arrangements that may beutilized to drive any of the. crystal. plates described herein: inharmonic mode. longitudinal vibrations along the length dimension In. Asillustrated in Fig. developed form, the; harmonic modeelectrodeand'connection platings be such as to leave three edge-sot the;crystal body t entirely free or any nlatingz'in order. to. makeedge;grinding ad justments of the frequency and the temperature coeficient offrequency.

The harmonic mode crystal plates I described herein may bemounted in anysuitable manner such as, for example, by clamping the electroded crystalplate I between a pair of opposite conductive clamping projections 5which may contact the electroded crystal plate I at opposite points ofvery small area designated 8 in Figs. 2 and 4. As. an illustrativeexample, an evacuated holder of the type disclosed in United StatesPatent No. 2,203,486, granted June 4, 1940, on application Serial No.248,437, filed December 30, 1938. by W. L. Bond may be utilized for thispurpfi -t Alternatively, the electroded crystal plate I may be.supported and electrically connected by soldering or otherwise attachingelectrically conductive spring wires to one or more pairs or any pairsuch as the middle pair of the crystal electrodes 4, at the oppositenodal points designated 6 in Figs. 2 and 4. Such conductive wires maysupport and hold the electroded crystal plate I in spring suspension.

It will be understood that any holder which will give stability and arelatively high reactance-resistance ratio, Q, may be used to mountthese harmonic model crystals.

The desired resonant frequency of the harmonic mode crystal plate I isa. function of the X axis length dimension L and of the several equalelementary or fundamental lengths l, the over-all length L. being equalto the n times the elementary length dimension I where n is thenumerical order of the harmonic as determined by the number of pairs ofopposite electrodes 4 that. are. applied to the major faces. 2 and 3 ofthe crystal plate I of any to angle. Since the invention may be adaptedto any order harmonic operation, odd or even, the. correlated values offrequency and dimensional ratio corresponding to the angle selected, aregiven hereinafter in terms of the width dimension W and the'elementarylength dimensions Z. It will be noted that. in so far as the elementaryareas are concerned, the related values of the orientation, thedimensional ratio and the frequency constant of the several elementaryareas of the harmonic mode crystals of this application: are the samevalues for any order of harmonic.

Fig. 6 is a graph giving the calculated values of frequency inkilocycles per second per centimeter or elementary length. dimension Zof the crystal plate I:- forall; angles of go from to +90. degrees, theangle 0. being always equal to 45 (or 135.). degrees. for: every angle:of. (p. For any given angle: of '(p the; curve. of Fig. 6 gives theapproximate frequency constant corresponding thereto. in terms offrequency in kilocycles per second; per centimeter of' the elementarylength dimension Z1 of the crystal: plate I. or n times this value wheren is the numerical order of the harmonic frequency. Since the frequencyof the longitudinal mode. vibrations along the length 1 varies inverselyas the particular length dimension of-l involved, the value or Z incentimeters corresponding to the resonant frequency in kilocycles. persecond. may be obtained directly from the frequency constant" given bythe curve of Fig. 6 for any valueof the angle (p selected. Thesecalculated values of resonant frequency approximate the-measured values.

The curve ofFig. 7 gives theorientation angles of r and thecorresponding dimensional ratiosthat" may be used to-constructquartaplates- I- to obtain a low or substantially. zero temperatureooei'licient of frequency for any order of .harmonic. The dimensionalratios are therein given in terms of the width dimension W and the fun+damental or elementary length dimension Z of the crystal plate I, theelementary lengthdimension Z of each of the elementary areas of thecrystal plate being equal toL/n Where L is the over-all .lengthdimension of the crystal. plate I and n is thenumerical order of theharmonic such as thesecond, third, fifth, etc. harmonic; .The curve ofFig. 7 gives the dimensional ratios in terms of three times theelementary length Z with respect to the width W for all of thecorresponding positive angles of between about +44 and +53degrees, theangle in every case being about 45 degrees as illustrated in either Fig.2 or Fig. 3. The angles of outside of the range given in Fig. 7 do notproduce the substantiallyzero temperature coeflicient of frequency.

The corresponding frequency constants for the quartz plates I, orientedand dimensioned in accordance with the values given by the curve of Fig.7 are substantially given by the curve of Fig. 6 at the intercept ofthe. particular value of (p selected. For example, when is substantially+44 30', 0 being substantially 45 degrees, and the dimensional ratio ofthree times theelementary length Z with respect to the width W of thequartz plate I is substantially 0.9394 as indicated by the curve of'Fig. 7, the frequency constant is about 340 kilocycles per second percentimeter of elementary length dimension Z or n times this value percentimeterof overall length dimension L where n is the numerical orderof the harmonic involved such as 2,3, 5, etc. For example, a fifthharmonic quartz crystal plate I of such an orientation and dimensionalratio and of one centimeter over-alllength L will have a resonantfrequency-of about five times 340 or about 1700 kilocycles per secondwhich remains substantially constant throughout a range of temperaturesfrom. about 5 C. to 45 C., the mid-temperature of the constant frequencytemperature range being about +25 C. V

Other'values of corresponding orientation, dimensional ratio andfrequency for crystal plates I that give a low or substantially zerotemperature coefficient of frequency may be obtained from the curves ofFigs. 6- and' 7 for any angle of go selected betweenabout +44 and +52degrees. It will be noted that for any given angle of (p, thedimensional ratio of the elementary area of these harmonic type crystalsfor the low or substantially zero temperature coefficient offrequency'is independent of what harmonic is used on the lengthvibration, the Width dimension W being slightly larger than three timesthe length Z of the fundamental element of the crystal plate I.Accordingly, a third harmonic mode crystal plate of a positive anglefrom+44 to +51 degrees has a total length L a little less than the widthdimension W of'the crystal; and for the same angles of (p, fifthharmonic mode crystals have an over-all length dimension L that isgreater than the width dimension W.

The curves of Figs. 6 and 7 illustrate the corresponding values ofresonant frequency, dimensional ratio and orientation angle that may beused in the angle'region of +45 degrees to obtain harmonic longitudinalmode quartz crystal plates I giving a very constantfrequencycharacteristic above and below the mean "0l midtemperature values fromabout 0 to 50 C. when usedin a circuit which operates the crystal plateI at or near its resonant frequency such as'for example an oscillatorcircuit of the type dis closed in. United States Patent No. 2,163,403,granted June 20, 1939 to L. A. Meacham anddiscussed in a paper publishedby L. A. Meacham in .The Proceedings of the Institute of RadioEngineers, vol. 26, No. 10, October 1938, page 1278. When the crystalplate I is used in the grid-filament circuit of a, non-inductivelycoupled Pierce oscillator circuit, the values given are nearly the samesince this circuit also operates the crystal near its resonant frequencyand hence produces the. nearly flat or constant frequency-temperaturerelationship- When used in such circuits which operate the crystal plateI at or very near the harmonic longitudinal mode resonant frequency, foran angle of (p of substantially +4430, the characteristic curve of theharmonic mode longitudinal reso nant frequency as a function oftemperature is substantially flat throughout a range of temperaturesfrom about 5 C. to 45 C. in the region above and below about 25C.; whilefor an angle of c of +45 degrees, the characteristic curve of frequencyas ,a function of temperature is'flat within the range of temperaturesbetween 28 C. and 72 C.

. When the crystal element I is driven in the harmonic mode longitudinalvibrations along the length dimension L by means of'a number of pairs ofopposite electrodes 4 corresponding in number of pairs to the order ofthe harmonic with suitable interconnections therebetween, the resultingvibrations consist of harmonic longitudinal or extensional vibrationsset up along the length dimension L of the crystal plate I which tend toset up vibrations also along the width dimension W of the crystalelement. The force system so set up is favorable for the so-called bulgetype of vibration and hence the possibility exists that the vibrationalong the wide dimension W which is mechanically coupled to the harmoniclongitudinal vibration along the length L is a third overtone bulgevibration when the elementary face area has the dimensional ratio of3L/n with respect to the width W of about 0.935 to 0.94 as given by thecurve of Fig. 7. There is a strong coupling between such widthvibrations and the desired harmoniclongitudinal vibration resonantfrequency. Accordingly, for any angle of (p, the mode of vibrationisdescribed herein as a coupled mode consisting of longitudinal harmonicmode vibrations along the length dimen-' sion L coupled with edge bulgemode vibrations along the width dimension'W; The frequency constantsforthe desired harmonic longitudinal mode are given in Fig. 6 for everyangle of 0, and approximate the measured values.

The proper dimensional ratio of the crystal plates described, operatesto produce the low or substantially zero temperature coefficient offrequency at a given temperature and the orientae tion angle (p controlsthe slope of the temperature-frequency characteristic, the slope beingnearly horizontal and flat in the (p angle regionof substantially +4430'. It will be noted that for crystals having an angle of (p of about+4430' a 0 angle'of about 45degrees, and a dimensional ratio as given bythe curve of Fig. 7 of about 0.9394, for three times the elementallength I with respect to thewidth W, the frequency constant as givenbythe curve of Fig. 6 is about 340.4 kilocycles'per second per centimeterof elemental length dimension Zor five times this value for the fifthharmonic of the longitudinal vibration along the length L. Thus a fifthharmonic crystal plate I having a length dimension L of 17.29millimeters, a width W of about 11.04 millimeters and a thickness T ofabout 0.5 millimeter will have a fifth harmonic resonant frequency ofabout 984,612 cycles per second or 1702.4 kilocycles per second percentimeter of over-all length dimension L. 1

By a slight change in the e angle of +44 30 and in the correspondingdimensional ratio as given by the curve of Fig. 7, the mid-temperatureof the constant frequency-temperature range may be shifted and raised orlowered as desired. For example, as shown in Figs. 6 and 7, when theangle (p is about +45 degrees, the dimensional ratio of three times theelementary length l with respect to the width W about 0.9356, and thefrequency about 340 kilocyeles per second per centimeter of elementarylength 1, then the mid-temperature of the constant frequency-temperaturerange from 28 C. to 72 C. is about +50 C.

Other values of corresponding dimensional ratio and frequency constantas a function of the angle (p may be similarly obtained from the curvesof Figs. 6 and 7. For example, a third harmonic quartz crystal plate Ihaving a e angle of +49 degrees and a (p angle of 45 degreesmay have, asgiven by the curve of Fig. 7, a ratio of 3l/W equal to about .936 and,for examplaa length dimension L of 30.? millimeters and a widthdimension W of-32.85 millimeters to obtain a zero temperaturecoefficient third harmonic resonance frequency of about 324,005 cyclesper secend, with a ratio of capacities of the order of 400, and a seriesinductance of about .92 henry if the thickness dimension T is .4millimeter. As another example, a fifth harmonic quartz crystal plate Ihaving a angle of about +49 degrees, a angle of about 45 degrees, alength dimension of 32.0 millimeters and a width dimension of 20.48millimeters thus giving a dimension ratio of 3l/W equal to 0.936 may beutilizedto attain a zero temperature coefiicient fifth harmonicresonance frequency of about 521,000 cycles per second with a ratio ofcapacities of the order of 600, and an inductance of about .518 henryfor a thickness dimension of .4 millimeter.

A seventh or other higher order harmonic crystal element I may besimilarly constructed by suitably proportioning the dimensional ratiosof width W, length L to obtain a zero temperature coefficient from thedesired harmonic longitudinal mode frequency along the length dimensionL relatively free from interfering modes of vibration.

Any undesired resonances that may b due to flexure modes may be removedby adjusting the ratio of the thickness dimension Twith respect to thelength dimension L without changing the desired harmonic longitudinalmode frequency or its zero temperature coefficient. Suchcrystal elementsmay be employed, for example, in a high frequency high-pass filter ofsharp cut-off where any extraneous resonance will come in the attenuatedband where it will-do no particular harm.

The frequency and the temperature coefficient of frequency of any ofthese crystal plates may be adjusted to relatively precise values byedge grinding on the edges along the width W and length L of the crystalplate. Since the frequency is controlled mainly by the X'" axis lengthdimension L, the frequency of a slightly oversize crystal plate I may beincreased by grinding on either of the edges perpendicular to the lengthdimension L thereby reducing the length dimension L and increasing thefrequency to a valu a few cycles under the desired frequency. Then bygrinding on either of the longest edges perpendicular to the widthdimension W, the width dimension W may be uniform- 1y reduced therebychanging the dimensional ratio of each of the elementary areas of thecrystal plate I until the desired lowest value of the temperaturecoefiicient of frequency is obtained. The frequency will have beenraised slightly by this last step of reducing the width dimension W. Ifthe frequency is still too low, it may be slightly raised by againreducing the length dimension L, and then the width dimension W may bagain readjusted to obtain the desired lowest value of temperaturecoefficient of frequency. By this process of edge grinding, both thefrequency and the temperature coefficient of. frequency of the crystalplate I may be ultimately adjusted to the correct or desired value. Inaddition to these adjustments, the frequency if too high may be loweredslightly by slightly concaving either of the major faces 2 or 3 of thecrystal plat I along the width dimension W midway between the ends ofany of the elementary lengths Z; and the temperature coefficient offrequency may be lowered and rendered more negative by slightlyconcaving either of the major faces 2 or 3 centrally along the entirelength dimension L.

The temperature coeflicient of frequency and the frequency of thesecrystals having a e angle in the region of +44 may be so adjusted thattheir temperature coefficients of frequency are less than 1 part in 10million per degree C.

and that their frequency is within ,5 parts in a million. Using suchcrystals in an oscillator circuit of the typ described in United StatesPatent No. 2,163,403 granted on.June 20, 1939 to L. A. Meacham, thefrequency of such oscillators may be held to 1 part in a million withouttemperature controland to 1 part in 10 million with a rough temperaturecontrol. After the initial aging period which may be of several weeks,the long period accuracy may be of the same order of magnitude. Suchoscillators are useful in single side-band radio systems, in broadcastsystems, and for many other purposes.

These harmonic longitudinal mode crystals of low or substantially zerotemperature coefficient of frequency may be used also in wide bandfilters at radio frequencies up to 2 megacycles per second or more withsubstantial freedom from troublesome subsidiary or extraneousresonances. Wide band quartz crystal filters have heretofore been,limited to about 500 kilocycles per second due to the extra. resonancesexisting in high frequency crystals. In carrier systems, it is oftendesirable to have highand low-pass filters of very sharp selectivity forthe purpose of dropping off supergroups at intermediate points and henceto have crystals which can be used in wide band filters at frequenciesup to 2 megacycles per second or more and which have relatively lowimpedance, low temperature coefficient of frequency, and vibrate at high.frequencies withthe desired frequency of vibration separated as much aspossibl from the frequencies, Any nearby undesired reson-. ance that ispresent may, if caused by a flexure.

of other modes.

ing' the desired resonance frequency or its temperatur coefficient.Otherwise, the thickness dimention 'I' of the crystal plate I mayordinarily be of the order of 1 millimeter more or less for example, orof other value to suit the impedance or other requirements of theparticular circuit withwhich it may be associated.

Either third harmonic or fifth harmonic crystals, for example, may beused to advantage in oscillators or moderately high impedance filters.Assuming a thickness dimension T of about 0.4 millimeter, the inductancein the equivalent circuit ofthe crystal for the third and fifth harmonicfrequencies will be respec-' tively of the order of 2.35 'henries and1.56 henries independent of the frequencies. Such crystals may be usedin oscillator systems or in filter. systems upto 3 megacycles persecond, for

example. a

In the construction of crystals such as the harmonic mode crystal plateshaving a angle in the region of +44? 30, as described hereinbefore,

it is often difficult and expensive to adjust the temperaturecoefiicient of frequency thereof closer than 1 part in 10 million perdegree centigrade-by mechanical adjustments alone on the tive materialdeposited in a known manner upon the opposite major surfaces thereof.The adjustment of capacitance may be made by scraping off or otherwiseremoving part of f the silver coating until the desired values ofcapacitance and frequency are obtained. Although this invention has beendescribed and illustrated in relation tospecific arrangements, it is tobe understood that it is capable of application in other organizationsand is, therefore, not to be limited to the particular em bodimentsdisclosed, but only by the scope of the appended claims and the state ofthe prior art. What is claimed is: 1. A piezoelectric quartz crystalvibratory body having its opposite substantially rectangular major facessubstantially parallel to an X axis and inclined substantially +44" withrespect to the Z axis as measured ina plane substantially perpendicularto said major faces, the over-all length dimensionand the widthdimension of said major faces being inclined substantially .45 degreeswith respect to said X axis, said overall length dimension being ineffect divided into a plurality of equal length elementary lengths toform a plurality of elementary areas, each of crystal itself. 'When usedin' an oscillator which is not temperature controlled, such crystals maycause'achange in frequency'of :1 part in a million-if the temperaturechanges by :10 C., which change infrequency may be too large a variationfor some purposes. By using an electrical element which variesitsimpedance with temperature change, the temperature coeiiicient offrequency of the crystal circuit may be. controlled and adjusted to avalue considerably less than 1 part in 10 million for :10 0. change intemperature, andover-all variations in the frequency of an oscillatorthat may be associated therewith maybe considerably reduced.

For this purpose, as-illustrate'd in Fig. 4, a condenser- 1 maybeconnected in series circuit relation with the electroded crystal plate Ito said elementary lengths having a dimensional ratio of substantially0.3131 with respect to said width dimension.

' ratio of substantially 0.3131 with respect to said stillfurther-reduce the temperature coefficient of the desired resonantfrequency of the crystal. plate I; The condenser --1'may have a small.

capacitance of the order of 150 micro-microfarads more or less, forexample, and of itself have a temperature coefficient ofcapacitance ofsuch magnitude and sign as to balance that of the crystal plate andthereby reduce the over-all temperature coefficient of frequency of thecombination crystal element and condenser to an extremely small value,

This method for compensating the temperature coefiic'ients of frequencyof crystals by the use of seriesconnected temperature variablecondensers maybe used to obtain a very nearly zero over-all temperaturecoeflicient of frequency for the combined crystal and condenser, whenused with a crystal which'has a very low temperature coefficient offrequency and whenyit is desired to keep the frequency of the system 7within. about 1 part'rin 10 million per degree centigrade'without theuse'of temperature controlrappa'ratus.

A small trimmer consist'of 'a thin micashee't having conductive materialsuch as silver or other suitable conduccondenser of suitable capacitysay, for example,v of' the order of '20 micro microfarads more'or lessmay be connected in' parallel circuit relation with the electrode ter-'3 ratio of substantially 0.3131 with respect to said 60' 2. Apiezoelectric quartz crystal vibratory body having its oppositesubstantially rectangular major faces substantially parallel to an Xaxis and inclined substantially +44? 30 with respect to the Zaxis asmeasured in a plane substantially perpendicular to said major faces, theover-all length dimension and the width dimension of said major facesbeing inclined substantially 45 degrees'with respect to said X axis,said over-all length dimension being in effect dividedv into a pluralityof equal length elementary lengths to form a plurality of elementaryareas, each of said elementary lengths having a dimensional Widthdimension, the number of said elementary lengths being one of theintegers 2 to 5.

,3. A piezoelectric.quartzcrystal vibratory body having its oppositesubstantially rectangular major faces substantially parallel to an Xaxis andinclined substantially +4 l 3G with respect V tiallyperpendicular tosaid major faces, the overto the Z axis as measured in aplane substanall length dimension and the width dimension of said majorfaces being inclined substantially 45-degrees with respect to said Xaxis, said overall length dimension being in effect divided into aplurality 'of equal length elementary lengths toform a plurality ofelementary areas, each of said elementary lengths having a dimensionalwidth dimension, and electrodes adjacent each of "said elementary areasof said major faces of said crystal-body. V

' 4. ,A piezoelectric quartz crystal vibratory body having its oppositesubstantially rectangular major faces substantially parallel to an Xaxis and inclined substantially +4 30 with respect to'the Z axis asmeasured ina plane substantially perpendicular to said major faces, theover-all 'length dimension and the width dimension of said major facesbeing inclined'sub'stantially 45 degrees .with respect to said X axis,said over-all lengthdimension'being in effect divided into apluralityofequal length elementary lengths to form aplurality ofelementary areas, each of said ekmentary lengths having a dimensionalratio of substantially 0.3131 with respect to said width dimension,means including electrodes ad jacent said elementary areas of said majorfaces for operating said crystal body in harmonic mode vibrations, and acondenser connected in series circuit relation with said electrodedcrystal body.

5. A piezoelectric quartz crystal vibratory body having its oppositesubstantially rectangular major faces substantially parallel to an Xaxis and inclined substantially +44? 30 degrees-with respectto the Zaxis as measured in a plane substantially perpendicular to said majorfaces, the over-all length dimension and the Width dimension of saidmajor faces being inclined substantially 45 degreeswith respect to saidX axis, said over-all length dimension being in effect divided into aplurality of equal length elementary lengths to form a plurality ofelementary areas, each of said elementary lengths having a dimensionalratio of substantially 0.3131 with respect to said width dimension, andmeans including electrodes formed integral with said elementary areas ofsaid major faces for operating said crystal body in a mode of motionconsisting substantially of harmonic longitudinal vibrations along saidlength dimension mechanically coupled with transverse vibrations alongsaid width dimension.

6. A quartz piezoelectric body of low temperature coefiicient offrequency adapted to vibrate at a harmonic frequency dependent mainlyupon the length dimension thereof, said body having a major plane ofsubstantially rectangular shape, said major plane being substantiallyparallel to an X axis and inclined with respect to the Z axissubstantially +44 30' as measured in a plane perpendicular to said majorplane, said length dimension and the width dimension of said major planebeing inclined substantially 45 degrees with respect to said X axis,said length dimension arithmetically divided by the numerical order ofsaid harmonic frequency being related to said width dimension in theratio of substantially 0.3131.

7. A piezoelectric quartz crystal body adapted to vibrate at a harmonicfrequency dependent mainly upon its length dimension, the major plane ofsaid body being substantially parallel to an X axis and inclinedsubstantially +44 30' with respect to the Z axis as measured in a planeperpendicular to said major plane, said length dimension and the Widthdimension of said may or plane being inclined substantially 45 degreeswith respect to said X axis, said length dimension arithmeticallydivided by the numerical order of said harmonic frequency beingsubstantially 0.3131 of said width dimension, said frequency beingsubstantially 340 kilocycles per second per centimeter of said lengthdimension arithmetically multiplied by said numerical order of saidharmonic frequency.

8. A piezoelectric quartz crystal plate having substantially rectangularmajor faces and means including a plurality of pairs of electrodesdisposed adjacent said major faces for operating said crystal plate atone of its harmonic frequencies third and fifth dependent mainly uponthe length dimension of said major faces, said pairs corresponding innumber to the numerical order of said harmonic and being disposed alongthe equal elementary lengths of said major axis dimension, said majorfaces being substantially parallel to an X axis and inclinedsubstantially +44 30 with respect to the Z axis as measured in a planeperpendicular to said major faces, said length dimension of said majorfaces being inclin'ed substantially 45 degrees with respect to said Xaxis, the dimensional ratio of each of said elementary lengths withrespect to the width dimension of said major faces being substantially0.3131.

- 9. A piezoelectric quartz crystal body of low or substantially zerotemperature coefficient of frequency adapted to vibrate at a harmonicfrequency dependent mainly upon each of the fundamental or elementarylength dimensions along the length dimension of said body multiplied bythe numerical order of said harmonic frequency, the major plane of saidbody being substantially rectangular, disposed substantially parallel toan X axis and inclined at an angle with respect to the Z axis, saidlength dimension of said major plane being inclined substantially 45degrees with respect to said X axis, said angle and the correspondingdimensional ratio of each of said elementary length dimensions withrespect to the width dimension of said major plane being substantiallythose values given by the curve of Fig. 7, and the frequency for each ofsaid elementary length dimensions being given by the curve of Fig. 6 atthe intercept for said angle.

10. A piezoelectric quartz crystal body, the length dimension of saidbody being divided in effect into equal elementary lengths in accordancewith the numerical order of a harmonic selected to obtain harmonic modevibrations along said length dimension, the major faces of said bodybeing substantially rectangular, substantially parallel to an X axis andinclined at an angle with respect to the Z axis, said length dimensionbeing inclined substantially 45 degrees with respect to said X axis, thedimensional ratio of said elementary lengths with respect to the Widthdimension of said major faces of said body being a selected value, saiddimensional ratio, said angle and said frequency being such relatedvalues as given by the curves of Figs. 6 and 7 as to obtain a low orsubstantially zero temperature coeflicient of frequency for saidharmonic mode vibrations.

11. A piezoelectric quartz crystal body of low temperature coefficientof frequency adapted to vibrate in a mode of motion consisting mainly oftwo coupled vibrations, one along the length dimension and the otheralong the width dimension of the major plane thereof, and at a harmonicmode frequency dependent upon the elementary length dimension equal tosaid length dimension arithmetically divided by the numerical order ofsaid harmonic, said frequency being given by the curve of Fig. 6 for theangle corresponding to the angle given by the curve of Fig. 7, saidmajor plane being of substantially rectangular shape, disposedsubstantially parallel with respect to an X axis and inclined at saidangle with respect to the X axis, said length dimension of said majorplane being inclined substantially 45 degrees with respect to said Xaxis, said angle and the dimensional relation between said widthdimension and said elementary length dimension being substantially thosevalues given by the curve of Fig. 7.

12. A piezoelectric quartz crystal body adapted for longitudinalvibrations along and at a harmonic frequency dependent mainly upon theelementary lengths of the length dimension of its substantiallyrectangular major plane, said major plane being substantially parallelto an X axis and inclined at an angle between substantially +44 and +51degrees with respect to the Z axis as measured in a plane perpendicularto said major plane, said length dimensionbeing inclined substantially45 degrees with respect to said X axis, the dimensional ratio of each ofsaid elementary or fundamental lengths of said length dimension withrespect to the width dimension of said major plane being betweensubstantially 0.311 and 0.314, said angle and said dimensional ratiohaving such relative values as to provide a low or substantially zerotemperature coefficient for said harmonic frequency. v

13. A piezoelectric quartz crystal body adapted for longitudinalvibrations along and at a fifth harmonic frequency dependent mainly uponthe elementary lengths of the length dimension of its substantiallyrectangularmajor plane, said major plane being substantially parallel toan X axis andinclined at an angle between +44 and +51 degrees withrespect to the Z axis as measured in a plane perpendicular to said majorplane, said length dimension axis being inclined substantially 45degrees with respect tosaid X axis, the dimensional ratio of each ofsaid elementary or fundamental lengths ofsaid major axis lengthdimension with respect to the width dimension being betweensubstantially 0.311 and 0.315, said angle and said dimensional ratiohaving such relative values as to produce a low or substantially zerotemperature coeflicient of frequency for said fifth harmonic frequency.

WARREN P. MASON.

